Question

a Boat goes 24 km upstream and 28 km downstream in 6 hours if goes 30 km upstream and 21 km downstream in 13/2 hours find the speed of boat in still water and also speed of the stream

plz gys answer this.......

Answer 1

let the stream in still water be x km/hr
and let the stream in stream be y km/hr

we know that t=d/s or d/s=t
and upstream=x-y km/hr
downstream=x+y km/hr
according to condition 24/x-y+28/x+y=6.......(i)
and 30/x-y+21/x+y=13/2.......(ii)
let 1/x-y=a and 1/x+y=b
so,
24a+28b=6.....(iii)
30a+21b=13/2.....(iv)
and u can use any method to solve this and 
substitue the values of a and b by
1/x-y=a and 1/x+y=b
and u will get equations in the form of x and y 
and u can solve it by any method 

i hope it helps!!!

Answer 2

Let the speed of boat in still water be x km/h
and the speed of the steam be y km/h

Than, Speed of boat in downstream =(x+y) km/h
Also, Speed of boat in upstream =(x-y) km/h

So, According to question,
$\frac{24}{x - y} + \frac{28}{x + y} = 6$
$\frac{30}{x - y} + \frac{21}{x + y} = \frac{13}{2}$

let the m = 1/x-y
and n = 1/x+y

Than, 24m + 28n = 6
12m + 14n =3
6m + 7n = 3/2.............(1)
and, 30m + 21n = 13/2
10m + 7n = 13/6...........(2)

Using equation 1 & 2, we get
10m-6m +7n-7n = 13/6 - 3/2
4m + 0n = 13-9/6
4m = 3/6
4m = 1/2
m = 1/8 ...........(3)

From equation 1, we get
6m + 7n = 3/2
6/8 + 7n = 3/2
3/4 + 7n = 3/2
7n = 3/2 - 3/4
7n = 6 - 3/4
7n = 3/4
n = 3/28 ............(4)

Putting the value of m and n from equation 3 and 4, we get
1/x-y = m
1/x-y = 1/8
x-y = 8 ................(5)

And,
1/x+y = n
1/x+y = 3/28
3x + 3y = 28 .................(6)

From equation 5, we get
3(x-y) = (8*3)
3x - 3y = 24 ...................(7)

Using equation 6 &7, we get
3x + 3x - 3y + 3y = 28 +24
6x = 52
x = 52/6
( x = 26/3 )

And, x - y = 8
- y = 8 - 26/3
- y = 24 - 26/3
( y = 2/3 )

Hence, the speed of boat in still water is 26/3 km/h and speed of the stream is 2/3 km/h